Question

Please help me with this question. Thanks

Answer 1

Look below

Explanation:

Rewrite using exponents

a.

`4\cdot 4\cdot 5\cdot 5\cdot 5\\\\= 4^2 \cdot 5^3`

b.

`3\cdot 3\cdot 3\cdot 3\cdot 3\cdot y\cdot y\\\\= 3^5 \cdot y^2`

c.

`(6x)(6x)(6x)(6x)\\\\= (6x)^4`

Simplify each expression ;

a.

`6^5\\= 6\cdot 6\cdot 6\cdot 6\cdot 6\\\\=7776`

b.

`((2)/(3) )^3\\\\\mathrm{Apply\:exponent\:rule}:\quad \left((a)/(b)\right)^c=(a^c)/(b^c)\\\\\left((2)/(3)\right)^3=(2^3)/(3^3)\\\\=(2^3)/(3^3)\\\\=(8)/(27)`

c.

`(2+3)^4\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\mathrm{Calculate\:within\:parentheses}\:\left(2+3\right)\::\quad 5\\\\=5^4\\\\\mathrm{Calculate\:exponents}\:5^4\: ;\: 5\cdot 5\cdot 5\cdot 5\\:\quad 625`

d.

`2(-(1)/(2) + (3)/(4) )^3\\\\\left(-(1)/(2)+(3)/(4)\right)^3=(1)/(4^3)\\\\=2\cdot (1)/(4^3)\\\\\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)\\\\=(1\cdot \:2)/(4^3)\\\\=(2)/(4^3)\\\\\mathrm{Factor}\:4^3:\quad 2^6\\=(2)/(2^6)\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=(1)/(2^5)\\\\=(1)/(32)`