Question

Which expression(s) are equivalent to (5^(1/8) x 5^(3/8))³?

a) 5¹/2
b) 5¹/4
c) 5¹/16
d) 6²/17

Answer 1

The equivalent expression to (5^(1/8) x 5^(3/8))³ is 5¹/2.

Step-by-step explanation:

The expression (5^(1/8) x 5^(3/8))³ can be simplified by using the laws of exponents. When multiplying two exponential terms with the same base, we can add their exponents. So, we have (5^(1/8 + 3/8))³ = (5^(4/8))³.

Next, we can simplify the exponent by dividing both the numerator and the denominator by their greatest common factor, which is 4. So, (5^(4/8))³ = (5^(1/2))³.

Finally, we can apply the property of raising a power to a power by multiplying the exponents. Therefore, (5^(1/2))³ = 5^(1/2 x 3) = 5^(3/2), which is equivalent to option a) 5¹/2.