Question

Give me 5 difficult questions with answers about Fatorisation of exponents. It should not be easy.
Best one will be marked as Brainliest.

Answer 1

1) (a^3)^2 * (b^2)^3 * (a^3) * (b^2) / (a^12) * (b^12) * (a^2) * (b^3) = ?

2) (√a³) * (∛b²) * ((√c)²)³ / (∛a) * (√b) = ?

3) ((((a²)³)^4)^5)^6 = ?

4) (√a(√a(√a(√a......) = ?

5) (∛a(∛a(∛a(∛a........) = ?

HERE IS WHAT YOU ASKED.
HOPE IT HELPS.

Answer 2

No. 1
${x}^{19} - {x}^{17} + {x}^{10 } + {x}^{8} + 1$

=x^3×(x^8)^2-x×(x^8)^2+x^2×(x^8)+(x^8)+1

let x^8 be @

=x^3×@^2-x×@^2+x^2×@+@+1

=x@^2(x^2-1)+@(x^2+1)+1

=x@^2(x-1)(x+1)+@{x(x-1)+(x+1)}+1

=x@^2(x-1)(x+1)+x@(x-1)+@(x+1)+1

=x@(x-1){@(x+1)+1}+1{@(x+1)+1}

=(@x+@+1){x@(x-1)+1}

=(x^9+x^8+1){x^8(x^2-x)+1)

=(x^9+x^8+1)(x^10-x^9+1)

No.2
$(b + c) ( c+ a)(a + b) + abc$

=(bc+ab+c^2+ca)(a+b)+abc

=abc+b^2c+a^2b+ab^2+c^2a+bc^2+a^2c+abc+abc

=(a^2b+a^2c+abc)+(b^2c+b^2a+abc)+(c^2a+c^2b+abc)+(c^2a+c^2b+abc)

=a(ab+ac+bc)+b(bc+ab+ac)+c(ca+bc+ab)

=(ab+bc+ca)(a+b+c)

Sorry for just two answer but this two are quite tough.

Hope it helped.