An exponent outside parentheses reaches every factor in the product. A rational exponent such as means take a cube root, then square; when a power is raised to another power, multiply the exponents. Rewrite the number and each variable factor separately, then use Desmos to check your result. Don't multiply the number by instead of raising it to that power.
Hints
- Hint 1
The power-of-a-product rule gives the outside exponent to every factor, including the number. What happens when you give separately to , , and ?
- Hint 2
In a rational exponent, the denominator names the root and the numerator names the power. For , take the cube root of , then square it. Don't multiply by .
- Hint 3
For a power of a power, multiply the exponents: . Do the same multiplication for before putting the factors back together.
Step-by-step
Apply the exponent to each factor
Step 1Give the outside exponent to every factor
A factor is one part of a product. Inside the parentheses, the factors are , , and . The outside exponent reaches all three factors, so write:
- Step 2
Evaluate the number factor
The rational exponent means take a cube root, then square. Since , evaluate the number factor:
- Step 3
Find the exponent on
For a power of a power, multiply the exponents. Apply to the existing exponent :
- Step 4
Find the exponent on
The factor also has an existing exponent. Multiply it by ; don't replace it with :
- Step 5
Rebuild and check the expression
Keep the three results multiplied. For a Desmos check, choose : is positive and a perfect cube, while would hide mistakes in the variable exponents. Type the lines shown. Desmos prints for both expressions. That check catches arithmetic slips; the exponent rules above show the expressions are equivalent for every positive and :
Choice B.