Solve: Multiply x to the 1 fourth power times x to the 5 eighths power.

Solution:

Given, multiply x to the 1 fourth power times x to the 5 eighths power.

We have to solve the given expression.

x to the 1 fourth power = x^1/4

x to the 5 eighths power = x^5/8

Multiply x to the 1 fourth power times x to the 5 eighths power = x^1/4 × x^5/8

Using the law of exponents,

a^m + aⁿ = a^{m + n}

Here, a = x

m = 1/4

n = 5/8

So, m + n = 1/4 + 5/8

= (2 + 5)/8

= 7/8

Now, x^1/4 × x^5/8 = x^7/8

Therefore, the required solution is x^7/8.

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Solve: Multiply x to the 1 fourth power times x to the 5 eighths power.

Summary:

The solution to the expression multiplying x to the 1 fourth power times x to the 5 eighths power is x^7/8.