Question

整式 积的乘方简便运算2^5×5^48^8×（-1/4）^12（-3）^5×（-2/3）^5×（-5）^6填空10^10

Answer 1

2^5×5^4=2×2^4×5^4=2×(2×5)^4=2×10^4=20000

8^8×(-1/4)^14=[8×(-1/4)]^8×(-1/4)^4=

(-2)^8×(-1/4)^4=[(-2)×(-1/4)]^4×(-2)^4=(1/2×2)^4=1

(-3)^5×(-2/3)^5×(-5)^6=[(-3)×(-2/3)]^5×(-5)^6=2^5×(-5)^6=[2×(-5)]^5×(-5)

=-100000×(-5)=500000

10^10×(1/10)^10=(10×1/10)^10=1

9-2009)^15×(1/2009)^14=[(-2009)×1/2009]^14×(-2009)=-2009