Question
How do you explain the answer four to the eighth power times four to the -8th power is equal to one
Answers
GPT-4o mini
To explain why \( 4^8 \times 4^{-8} = 1 \), we can use the properties of exponents.
One important property of exponents states that when you multiply two numbers with the same base, you add the exponents:
\[
a^m \times a^n = a^{m+n}
\]
In your case, we have:
\[
4^8 \times 4^{-8}
\]
Applying the property of exponents:
\[
4^8 \times 4^{-8} = 4^{8 + (-8)} = 4^{0}
\]
Now, according to another property of exponents, any non-zero number raised to the power of 0 is equal to 1:
\[
a^0 = 1 \quad \text{(for any } a \neq 0\text{)}
\]
Since \( 4^0 = 1 \):
\[
4^8 \times 4^{-8} = 4^0 = 1
\]
Thus, we conclude that:
\[
4^8 \times 4^{-8} = 1
\]
This shows that multiplying a number by its reciprocal (which \( 4^{-8} \) is in this case) results in 1, which is confirmed by the properties of exponents.
One important property of exponents states that when you multiply two numbers with the same base, you add the exponents:
\[
a^m \times a^n = a^{m+n}
\]
In your case, we have:
\[
4^8 \times 4^{-8}
\]
Applying the property of exponents:
\[
4^8 \times 4^{-8} = 4^{8 + (-8)} = 4^{0}
\]
Now, according to another property of exponents, any non-zero number raised to the power of 0 is equal to 1:
\[
a^0 = 1 \quad \text{(for any } a \neq 0\text{)}
\]
Since \( 4^0 = 1 \):
\[
4^8 \times 4^{-8} = 4^0 = 1
\]
Thus, we conclude that:
\[
4^8 \times 4^{-8} = 1
\]
This shows that multiplying a number by its reciprocal (which \( 4^{-8} \) is in this case) results in 1, which is confirmed by the properties of exponents.