What Is Negative 3 To The Third Power? | One Tiny Sign Flip

Negative three raised to the third power equals -27, because the base is 3 and an odd exponent keeps the minus sign.

If this expression has ever made you stop and squint at the page, you’re not alone. A lot of students know that 3 to the third power is 27, then get stuck on the minus sign. That tiny mark changes the feel of the problem, and it’s also where most mistakes happen.

The clean answer is -27. Still, the answer matters less than the reason behind it. Once you see why the sign stays negative here, expressions with powers stop feeling random. You can work them out with confidence instead of guessing.

This article breaks it down in plain math. You’ll see what “to the third power” means, why odd powers behave the way they do, and how parentheses can change the whole result. By the end, this one problem will feel simple enough to do in your head.

What Is Negative 3 To The Third Power? Step By Step

Start with the number 3. Raising a number to the third power means multiplying that number by itself three times:

3 × 3 × 3 = 27

Now bring back the negative sign. When people say “negative 3 to the third power,” they usually mean:

(-3) × (-3) × (-3)

Work through it one pair at a time. The first two negative signs make a positive:

(-3) × (-3) = 9

Then multiply by the last negative 3:

9 × (-3) = -27

So the full result is -27.

Start With What “To The Third Power” Means

The phrase “to the third power” means the number appears as a factor three times. You may also hear it called “cubed.” So 4 cubed means 4 × 4 × 4. In the same way, negative 3 cubed means negative 3 multiplied by itself three times.

That repeated multiplication is the whole story. There’s no mystery move, no hidden trick, and no new rule sneaking in. You’re just multiplying three copies of the same number.

Then Place The Minus Sign Correctly

This is where many students slip. A minus sign can be part of the base, or it can sit outside the power. Those are not always the same thing. In this problem, the negative sign belongs with the 3, so the base is -3.

Once the base is negative, each multiplication carries that sign with it. Since there are three factors, you end up multiplying an odd count of negative numbers. That leaves one negative sign in the final answer.

Why The Answer Is -27 And Not 27

The fast way to think about it is this: an odd number of negative factors gives a negative answer. An even number of negative factors gives a positive answer.

Here you have three factors of -3:

(-3) × (-3) × (-3)

Three is odd. So the answer stays negative.

You can also see it in motion. Multiply the first two factors and you get positive 9. Multiply that by one more negative 3 and the sign flips back to negative. That’s why the final result is not 27.

Odd Powers Keep A Negative Result

This is one of the handiest patterns in exponent work. If a negative base is raised to an odd power, the answer is negative. If the same negative base is raised to an even power, the answer is positive.

So:

• (-3)¹ = -3
• (-3)² = 9
• (-3)³ = -27
• (-3)⁴ = 81

The sign keeps flipping as the exponent rises. Odd power, negative result. Even power, positive result. That pattern lines up with standard exponent rules taught in OpenStax’s order of operations section, where exponents are handled before the rest of the expression.

Parentheses Change What The Exponent Touches

Parentheses tell you exactly what the exponent applies to. If you write (-3)³, the exponent applies to the whole negative number. If you write -3³, many teachers read that as the negative of 3 cubed, which still lands at -27 in this one case.

That can make students think the two forms are always interchangeable. They are not. Change the exponent to 2 and the difference jumps out:

• (-3)² = 9
• -3² = -9

Same digits. Different structure. Different answer.

Expressions That Look Similar But Mean Different Things

Math gets easier when you stop reading only the numbers and start reading the structure. A minus sign outside parentheses, a minus sign inside parentheses, and a power attached to one part of the expression can all lead to different results.

That’s why it helps to expand the expression into repeated multiplication when you feel stuck. It slows the problem down just enough to show what’s really happening.

Expression	What It Means	Value
33	3 × 3 × 3	27
(-3)3	(-3) × (-3) × (-3)	-27
-33	-(3 × 3 × 3)	-27
(-3)2	(-3) × (-3)	9
-32	-(3 × 3)	-9
(-3)1	One factor of -3	-3
(-3)4	(-3) × (-3) × (-3) × (-3)	81
-(−3)3	Negative of -27	27

That table shows why this topic trips people up. Some expressions look almost identical on the page, yet the exponent is not always acting on the same thing. Once you spot what the power touches, the answer gets a lot easier to trust.

A Fast Way To Check Your Work

You don’t need a long routine every time. A quick check can save you from the most common sign errors.

Use The Order Of Operations

Exponents come before multiplication, addition, and subtraction outside grouping symbols. So if the exponent sits on the 3 alone, cube the 3 first. If the exponent sits on (-3), then the whole negative number gets repeated three times.

This rule is one reason textbooks stress grouping symbols so much. The form on the page tells you how to read the expression. OpenStax’s section on integer exponents also shows that a negative sign in the base behaves differently from a sign that sits outside the power.

Test With Repeated Multiplication

If you’re unsure, rewrite the power as repeated multiplication. It feels slower at first, yet it cuts through confusion fast.

Take this expression:

(-3)³

Rewrite it as:

(-3) × (-3) × (-3)

Then multiply from left to right. You’ll see the sign pattern right away. This works not just for 3, but for any negative number raised to a small whole-number power.

Patterns With Negative Bases

Once you know one case, the rest fall into a pattern. Watch what happens as the exponent rises while the base stays at -3.

Power	Expanded Form	Result
(-3)1	-3	-3
(-3)2	(-3)(-3)	9
(-3)3	(-3)(-3)(-3)	-27
(-3)4	(-3)(-3)(-3)(-3)	81
(-3)5	Five factors of -3	-243

The sign alternates every time. Negative, positive, negative, positive. That happens because each new factor of -3 flips the sign again. The size of the number grows, and the sign switches back and forth.

That pattern is handy on tests. Even before you finish the multiplication, you can predict whether the answer should be positive or negative. If the exponent is odd, expect a negative result. If it’s even, expect a positive one.

Mistakes Students Make With Negative 3 Cubed

This problem is small, yet it catches a lot of people because the eye jumps to the 3 and the exponent, then skips over the sign details. Here are the usual slip-ups.

Mixing Up The Base And The Sign

Students often treat the negative sign like a decoration instead of part of the number. In (-3)³, the base is not just 3. The base is -3. That matters because every repeated factor carries the sign with it.

Once you see the whole base, the answer starts to make sense. Three negative factors can’t end positive, since one negative sign is left over after pairs cancel out.

Treating A Power Like Simple Multiplication

Another slip is reading (-3)³ as -3 × 3. That gives -9, which is not what the expression says. The exponent does not mean “times 3.” It means “use this number as a factor three times.”

That one shift in reading fixes a lot of exponent mistakes. Powers are about repeated multiplication of the base, not multiplication by the exponent.

When Teachers Write It In Different Ways

You may see this idea written as “negative 3 to the third power,” “negative 3 cubed,” “(-3) raised to the third power,” or “(-3)³.” In most classroom settings, those all point to the same value: -27.

Still, printed math can be strict about notation. If parentheses are present, read them carefully. If they are missing, use order of operations and the style your class has been taught. In a spoken question, teachers often mean the negative number itself is being cubed. On a worksheet, the symbols on the page decide it.

So if you’re ever caught between wording and notation, trust the written structure first. That keeps your answer tied to the expression instead of guesswork.

The Answer In One Clean Line

Negative 3 to the third power is -27. You get there by multiplying (-3) × (-3) × (-3), which turns into 9 × (-3), then -27.

Once that clicks, other exponent problems get less slippery. Read the base, watch the parentheses, and check whether the exponent is odd or even. That small habit will save you a pile of lost points.