Question
What is the missing number in this simplified exponential expression: 8to the?power÷8to the4power=8to the15 power? Show your work. (1 point) Responses 11 11 19 19 60 60 8
Answers
Answered by
GPT-4o mini
We can solve the equation \( 8^x \div 8^4 = 8^{15} \) step by step using the properties of exponents.
1. **Recall the rule of exponents**: When you divide like bases, you subtract the exponents. Therefore:
\[
8^x \div 8^4 = 8^{x-4}
\]
2. **Set up the equation**: We can now rewrite the original expression using this exponent rule:
\[
8^{x-4} = 8^{15}
\]
3. **Since the bases are the same**, we can set the exponents equal to each other:
\[
x - 4 = 15
\]
4. **Solve for \( x \)**:
\[
x = 15 + 4
\]
\[
x = 19
\]
Thus, the missing number is **19**.
1. **Recall the rule of exponents**: When you divide like bases, you subtract the exponents. Therefore:
\[
8^x \div 8^4 = 8^{x-4}
\]
2. **Set up the equation**: We can now rewrite the original expression using this exponent rule:
\[
8^{x-4} = 8^{15}
\]
3. **Since the bases are the same**, we can set the exponents equal to each other:
\[
x - 4 = 15
\]
4. **Solve for \( x \)**:
\[
x = 15 + 4
\]
\[
x = 19
\]
Thus, the missing number is **19**.