Flashcards ACT Math: Exponent Rules

What do an exponent and base represent?

The base is the number being multiplied, and the exponent indicates how many times the base is multiplied by itself.

What happens when you multiply powers with the same base?

You add the exponents.

Why do you add exponents when multiplying powers with the same base?

Because you are essentially combining the number of times the base is multiplied.

What happens when you divide powers with the same base?

You subtract the exponents.

Why do you subtract exponents when dividing powers with the same base?

Because you are removing the number of times the base is multiplied in the denominator from the numerator.

What happens when you raise a power to another power?

You multiply the exponents.

Why do you multiply exponents when raising a power to another power?

Because you are multiplying the base by itself multiple times, as indicated by the two exponents.

What does applying an outside exponent to every factor in parentheses mean?

You raise each factor inside the parentheses to the outside exponent.

What is the power of a product rule?

When you raise a product to a power, you raise each factor in the product to that power.

What is the power of a fraction rule?

When you raise a fraction to a power, you raise both the numerator and the denominator to that power.

What is x⁰ equal to?

x⁰ = 1 for any non-zero x.

What is the value of x¹?

x¹ = x.

What do negative exponents represent?

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent.

Why does a negative exponent not mean a negative answer?

A negative exponent indicates a reciprocal, which can still be positive if the base is positive.

What happens with negative bases and even exponents?

The result is positive.

What happens with negative bases and odd exponents?

The result is negative.

Why are parentheses important with negative numbers?

Parentheses clarify the order of operations and ensure correct calculations.

What are the three most important exponent rules?

1. Multiply powers: add exponents. 2. Divide powers: subtract exponents. 3. Power of a power: multiply exponents.

What are quick recognition prompts for exponents?

Look for patterns in multiplication and division of powers, and remember the rules for zero and negative exponents.

What does (4x³y⁴)² equal?

16x⁶y⁸.

What does ((4x³y⁴)²)/(2xy) equal?

8x⁵y⁷.

How do you simplify (x²)³?

You multiply the exponents to get x⁶.

What is the result of 5² × 5³?

5⁵, since you add the exponents.

What is the result of 7⁴ ÷ 7²?

7², since you subtract the exponents.

What is (2xy)²?

4x²y², since you square each factor.

What is (3a²b)³?

27a⁶b³, since you cube each factor.

What is 10⁻²?

1/10² or 1/100.

What is the value of (-2)³?

-8, since the base is negative and the exponent is odd.

What is the value of (-3)²?

9, since the base is negative and the exponent is even.

What does (x⁻²) equal?

1/x².

What does (a/b)⁴ equal?

a⁴/b⁴.

What is the result of (x²y³)(x⁴y²)?

x⁶y⁵, since you add the exponents.

What is the result of (2x²)²?

4x⁴, since you square the coefficient and the variable.

What is the result of (3x⁻²)²?

9x⁻⁴.

What is the result of (x⁰)?

1.

What is the result of 4⁰?

1.

What is the result of (xy)⁴?

x⁴y⁴.

What is the result of (2x)⁵?

32x⁵.

What is the result of (x²y)³?

x⁶y³.

What is the result of (3x²)⁴?

81x⁸.

What is the result of (x⁻³)⁻²?

x⁶.

What is the result of (2/x)²?

4/x².

What is the result of (x²y)⁴?

x⁸y⁴.

What is the result of (a/b)⁻²?

b²/a².

What is the result of (x²)⁰?

1.

What is the result of (2x)⁻³?

1/(2³x³) or 1/(8x³).

What is the result of (3x⁻²)⁰?

1.