第41页 - 经纶学典学霸七年级数学上下册【江苏国标】

A

12

4

±8

$ \begin{aligned}解：原式&=0.04²⁰²³×[(-5)²]²⁰²³ \\ &=0.04²⁰²³×25²⁰²³ \\ &=(0.04×25)²⁰²³ \\ &=1²⁰²³ \\ &=1. \\ \end{aligned}$

$ \begin{aligned} 解：原式&=(- \frac{12}{5} × \frac{5}{6} × \frac{1}{2})¹¹×\frac{1}{2} ×(-\frac{5}{6} )² \\ &=-\frac{1}{2} × \frac{25}{36} \\ &=-\frac{25}{72} \\ \end{aligned}$

$ \begin{aligned}解：原式&=0.125³×0.25³×4³×16³ \\ &=(0.125×0.25×4×16)³ \\ &=2³ \\ &=8. \\ \end{aligned}$

$解：因为(2×3)^{x+3}=36^{x+1}$

$所以6^{x+3}=6^{2(x+1)}$

$所以x+3=2(x+1)$

$ 解得x=1$

$解：因为(9²)³×(\frac{1}{3})⁸=4$

$所以3⁶×(a³)²×(\frac{1}{3})⁸=4$

$所以3⁶×(\frac{1}{3})⁶×(a³)²×(\frac{1}{3})²$

$=(3×\frac{1}{3})⁶×(a³)²×(\frac{1}{3})²$

$=4$

$所以(a³)²×\frac{1}{9}=4$

$所以(a³)²=36$

$所以a³=±6$

$ \begin{aligned} 解：(2^{2m+3n})^2&=(2^{2m}·2^{3n})^2 \\ &=(a^2b^3)^2 \\ &=a^4b^6 \\ \end{aligned}$

$解：因为m=8^9，n=9^8$

$ \begin{aligned} 所以72^{72}&=(8×9)^{72} \\ &=8^{72}×9^{72} \\ &=8^{8×9}×9^{8×9} \\ &=(8^9)^8×(9^8)^9 \\ &=m^8n^9. \\ \end{aligned}$

$解：能被13整除.理由如下:$

$因为5^2·3^{2n+1}·2^n-3^n·6^{n+2}$

$ =5^2·3^1·3^n·3^n·2^n-3^n·6^2·6^n$

$ =75·3^n·2^n·3^n-36·3^n·6^n$

$ =75·(3×2)^n·3^n-36·3^n·6^n$

$ =(75-36)·3^n·6^n$

$ =39·3^n·6^n$

$ 又因为39能被13整除$

$所以5^2·3^{2n+1}·2^n-3^n·6^{n+2}(n为正整数)$

$能被13整除.$

$解：c=a³b².理由如下:$

$ \begin{aligned}因为c⁵&=72 \\ &=8×9 \\ &=2³×3² \\ &=(a⁵)³ ·(b⁵)² \\ &=(a³b²)⁵ \\ \end{aligned}$

$所以c=a³b²$