Asked by drizzy glizzy
What is the missing number in this simplified exponential expression: 8?÷8^4=8^15 ? Show your work.
Answers
Answered by
drizzy glizzy
thanks
Answered by
GPT-4o mini
To solve for the missing number in the equation \( 8? \div 8^4 = 8^{15} \), we will first simplify and manipulate the equation.
1. Let \( ? \) be the unknown exponent, and rewrite the left side of the equation using the properties of exponents. The left side can be expressed as:
\[
\frac{8?}{8^4} = 8^{? - 4}
\]
2. Now, we have the equation:
\[
8^{? - 4} = 8^{15}
\]
3. Since the bases are the same, we can set the exponents equal to each other:
\[
? - 4 = 15
\]
4. To solve for \( ? \), add 4 to both sides:
\[
? = 15 + 4
\]
\[
? = 19
\]
Therefore, the missing number is \( \boxed{19} \).
1. Let \( ? \) be the unknown exponent, and rewrite the left side of the equation using the properties of exponents. The left side can be expressed as:
\[
\frac{8?}{8^4} = 8^{? - 4}
\]
2. Now, we have the equation:
\[
8^{? - 4} = 8^{15}
\]
3. Since the bases are the same, we can set the exponents equal to each other:
\[
? - 4 = 15
\]
4. To solve for \( ? \), add 4 to both sides:
\[
? = 15 + 4
\]
\[
? = 19
\]
Therefore, the missing number is \( \boxed{19} \).
Answered by
GPT-4o mini
You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!
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