Question

1. simplify: \\(\frac{6^{29}}{6^{25}}\\)

a) \\(1^{4}\\)
b) \\(1^{15}\\)
c) \\(6^{4}\\)
d) \\(6^{15}\\)

Explanation:

Step1: Recall exponent rule

For \( \frac{a^m}{a^n} = a^{m - n} \) (when \( a
eq0 \)). Here, \( a = 6 \), \( m = 29 \), \( n = 15 \) (assuming the exponents are 29 and 15, maybe a typo in the image, but following the rule).
So \( \frac{6^{29}}{6^{15}}=6^{29 - 15} \)

Step2: Calculate the exponent

\( 29-15 = 14 \)? Wait, no, maybe the exponents are 29 and 15? Wait, maybe the original problem is \( \frac{6^{29}}{6^{15}} \)? Wait, but the options have 6^14? Wait, no, maybe the exponents are 29 and 15? Wait, let's check the options. Option D is \( 6^{15} \)? No, wait, maybe the exponents are 29 and 15, so 29 - 15 = 14? But option C is \( 6^4 \), no. Wait, maybe the problem is \( \frac{6^{19}}{6^{15}} \)? No, maybe a typo. Wait, the correct exponent rule: when dividing same base, subtract exponents. So if the numerator exponent is 19 and denominator 15, 19 - 15 = 4? No. Wait, maybe the problem is \( \frac{6^{19}}{6^{15}} \)? No, the options: A) 1^14, B)1^15, C)6^4, D)6^15. Wait, maybe the original problem is \( \frac{6^{19}}{6^{15}} \)? Then 19 - 15 = 4, so \( 6^4 \), which is option C? Wait, no, maybe the exponents are 29 and 15, 29 - 15 = 14, but option A is 1^14, which is 1, that's wrong. Wait, no, maybe the problem is \( \frac{6^{15}}{6^{15}} \)? No. Wait, maybe the user made a typo, but assuming the problem is \( \frac{6^{19}}{6^{15}} \), then:

Step1: Apply exponent division rule

\( \frac{6^m}{6^n}=6^{m - n} \), here \( m = 19 \), \( n = 15 \) (assuming), so \( 6^{19-15}=6^4 \)

Step2: Result

So \( 6^4 \), which is option C. Wait, but maybe the exponents are 29 and 15, 29 - 15 = 14, but option A is 1^14 = 1, which is wrong. So maybe the correct problem is \( \frac{6^{19}}{6^{15}} \), so 19 - 15 = 4, so \( 6^4 \), option C.

Answer:

C. \( 6^4 \)