Answer :
Sure, let's simplify the expression \(6^7 \div 6^5\) step by step.
1. Rewrite the division using exponents: According to the properties of exponents, particularly the quotient rule \( \frac{a^m}{a^n} = a^{m-n} \), we can rewrite the given expression as:
[tex]\[ 6^7 \div 6^5 = 6^{7-5} \][/tex]
2. Subtract the exponents: Simplify the exponent in the expression:
[tex]\[ 6^{7-5} = 6^2 \][/tex]
3. Calculate the power: Now, calculate \(6^2\):
[tex]\[ 6^2 = 6 \times 6 = 36 \][/tex]
Therefore, the simplified value of the expression \(6^7 \div 6^5\) is \(6^2 = 36\).
So, the correct answer is C. 36.
1. Rewrite the division using exponents: According to the properties of exponents, particularly the quotient rule \( \frac{a^m}{a^n} = a^{m-n} \), we can rewrite the given expression as:
[tex]\[ 6^7 \div 6^5 = 6^{7-5} \][/tex]
2. Subtract the exponents: Simplify the exponent in the expression:
[tex]\[ 6^{7-5} = 6^2 \][/tex]
3. Calculate the power: Now, calculate \(6^2\):
[tex]\[ 6^2 = 6 \times 6 = 36 \][/tex]
Therefore, the simplified value of the expression \(6^7 \div 6^5\) is \(6^2 = 36\).
So, the correct answer is C. 36.
