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Given that 2^(h) xx 2^(3) = 2^(9), find ...

Given that `2^(h) xx 2^(3) = 2^(9)`, find the value of `h`.

A

3

B

6

C

8

D

12

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( 2^h \times 2^3 = 2^9 \) for \( h \), we can follow these steps: ### Step 1: Apply the property of exponents When multiplying two powers with the same base, we can add their exponents. Therefore, we can rewrite the left side of the equation: \[ 2^h \times 2^3 = 2^{h + 3} \] ### Step 2: Set the exponents equal Now, we have the equation: \[ 2^{h + 3} = 2^9 \] Since the bases are the same (both are base 2), we can set the exponents equal to each other: \[ h + 3 = 9 \] ### Step 3: Solve for \( h \) To find \( h \), we need to isolate it: \[ h = 9 - 3 \] \[ h = 6 \] ### Final Answer Thus, the value of \( h \) is \( 6 \). ---
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