Question Find the value of $x$ in the simplified expression $g^{x} + h^{-3} = \frac{1}{g^{6}} + \frac{1}{h^{3}}$ .

Studdy Solution

STEP 1

Assumptions
1. The expressions are given as $g^{x}+h^{-3}=\frac{1}{g^{6}}+\frac{1}{h^{3}}$ .
2. We need to find the value of $x$ .
3. The properties of exponents will be used to solve for $x$ .

STEP 2

Recognize that $h^{-3}$ is the same as $\frac{1}{h^{3}}$ by the definition of negative exponents.
$h^{-3} = \frac{1}{h^{3}}$

STEP 3

Since we have a term $\frac{1}{g^{6}}$ on the right side of the equation, we can rewrite $g^{x}$ in terms of a fraction with a negative exponent if it equals $\frac{1}{g^{6}}$ .
$g^{x} = \frac{1}{g^{6}} \implies g^{x} = g^{-6}$

STEP 4

Now that we have $g^{x} = g^{-6}$ , we can equate the exponents since the bases are the same and non-zero.
$x = -6$
The value of $x$ is $-6$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms