Name: Date:
Designed for 11th grade math students. Simplify each expression without using a calculator by rewriting powers as roots.
Evaluate 25^(1/2).
Evaluate 64^(1/3).
Evaluate 8^(2/3).
Evaluate 36^(-1/2).
Evaluate 32^(3/5).
Evaluate 81^(-3/4).
Evaluate (4/9)^(-3/2).
Simplify (x^(2/3)) * (x^(4/3)) into a single power of x.
Evaluate 25^(1/2).
5 (Take the square root of 25).
Evaluate 64^(1/3).
4 (Take the cube root of 64).
Evaluate 8^(2/3).
4 (The cube root of 8 is 2, and 2 squared is 4).
Evaluate 36^(-1/2).
1/6 (The square root of 36 is 6, and the negative exponent inverts it to 1/6).
Evaluate 32^(3/5).
8 (The fifth root of 32 is 2, and 2 cubed is 8).
Evaluate 81^(-3/4).
1/27 (The fourth root of 81 is 3, 3 cubed is 27, and the negative exponent makes it 1/27).
Evaluate (4/9)^(-3/2).
27/8 (Invert the fraction to 9/4, take the square root to get 3/2, then cube both numbers to get 27/8).
Simplify (x^(2/3)) * (x^(4/3)) into a single power of x.
x^2 (Add exponents: 2/3 + 4/3 = 6/3 = 2).
