Answer:
1. a
2. c
3. a
4. c
I think number 5 has an error
Step-by-step explanation:
1.
[tex] \rm \: 15625 = {5}^{x + 3} [/tex]
[tex]\implies \rm 15,625 = {5}^{x} \times {5}^{3} [/tex]
[tex]\implies \rm \: \frac{15625}{ {5}^{3} } = {5}^{x}[/tex]
[tex]\implies \rm \: 125 = {5}^{x}[/tex]
[tex]\implies \rm \: x = \frac{ log(125) }{ log(5) }[/tex]
[tex]\implies \rm \: x = \frac{ log( {5}^{3} )}{ log( {5}^{1} ) }[/tex]
[tex]\implies \boxed{ \rm \: x = 3}[/tex]
2.
[tex] \rm \: \frac{(x + y) {}^{2} }{(x + y) {}^{3} } \times \frac{(x + y) {}^{5} }{( x + y) {}^{6} } \times \frac{(x + y) {}^{8} }{(x + y) {}^{10} } [/tex]
[tex]\implies \rm \frac{(x+y)^2(x+y)^5(x+y)^8}{(x+y)^3(x+y)^6(x+y)^{10}}[/tex]
[tex]\implies \rm \frac{(x+y)^{2+5+8}}{(x+y)^{3+6+10}}[/tex]
[tex]\implies \rm \frac{(x+y)^{15}}{(x+y)^{19}}[/tex]
[tex]\implies \rm \frac{1}{(x+y)^{19-15}}[/tex]
[tex]\implies \boxed{\rm \frac{1}{(x+y)^4}}[/tex]
3.
[tex]\rm 729 = 9^{3x}[/tex]
[tex]\implies \rm 729 = (9^{x})^3[/tex]
[tex]\implies \rm \sqrt[3]{729}= \sqrt[3]{(9^{x})^3}[/tex]
[tex]\implies \rm 9 = 9^{x}[/tex]
[tex]\implies \boxed{\rm 1 = x}[/tex]
4.
3 × 3 × 3 × 3 × 3
Just count the threes
Since there are 5 threes, the exponent is 5.
Therefore 3 × 3 × 3 × 3 × 3 = 3⁵
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