7 answers
To simplify the expression \( 2^4 \times 2^2 \) using the Product Rule of Exponents, you add the exponents when multiplying like bases. The rule states:
\[ a^m \times a^n = a^{m+n} \]
Applying this to the given expression:
\[ 2^4 \times 2^2 = 2^{4+2} \]
Now, calculate the sum of the exponents:
\[ 4 + 2 = 6 \]
Thus, the expression simplifies to:
\[ 2^6 \]
So, \( 2^4 \times 2^2 = 2^6 \).
To simplify the expression \( 3^8 \times 3^3 \) using the Product Rule of Exponents, you add the exponents when multiplying like bases. The Product Rule states:
\[ a^m \times a^n = a^{m+n} \]
Applying this to the given expression:
\[ 3^8 \times 3^3 = 3^{8+3} \]
Now, calculate the sum of the exponents:
\[ 8 + 3 = 11 \]
Thus, the expression simplifies to:
\[ 3^{11} \]
So, \( 3^8 \times 3^3 = 3^{11} \).
To find the numerical equivalent of \( 7^2 \times 7^3 \), we can first apply the Product Rule of Exponents, which states:
\[ a^m \times a^n = a^{m+n} \]
So we have:
\[ 7^2 \times 7^3 = 7^{2+3} = 7^5 \]
Next, we calculate \( 7^5 \):
\[ 7^5 = 7 \times 7 \times 7 \times 7 \times 7 \]
Calculating step by step:
Thus, the numerical equivalent of \( 7^2 \times 7^3 \) is:
\[ 7^5 = 16807 \]
To find the numerical equivalent of \( 3^9 \times 3^{-5} \), we can use the Product Rule of Exponents, which states:
\[ a^m \times a^n = a^{m+n} \]
Applying this rule, we have:
\[ 3^9 \times 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^{4} \]
Now, let's calculate \( 3^4 \):
\[ 3^4 = 3 \times 3 \times 3 \times 3 \]
Calculating this step by step:
Thus, the numerical equivalent of \( 3^9 \times 3^{-5} \) is:
\[ 3^4 = 81 \]
