Question

which expression is equivalent to $6^0 \times \frac{6^5}{6^4}$? answer $\bigcirc$ 6 $\bigcirc$ 0 $\bigcirc$ 1 $\bigcirc$ $\frac{1}{6}$

Explanation:

Step1: Recall exponent rules

Any non - zero number to the power of 0 is 1, so \(6^{0}=1\). For the fraction \(\frac{6^{5}}{6^{4}}\), we use the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (where \(a
eq0\) and \(m,n\) are real numbers). Here \(a = 6\), \(m = 5\) and \(n = 4\), so \(\frac{6^{5}}{6^{4}}=6^{5 - 4}=6^{1}=6\).

Step2: Multiply the results

We have \(6^{0}\times\frac{6^{5}}{6^{4}}=1\times6\) (since \(6^{0} = 1\) and \(\frac{6^{5}}{6^{4}}=6\)).

Answer:

6