Answer:
1. 4096
2. [tex]\rm -\frac{75}{x^{14}}[/tex]
3. [tex]\rm -\frac{10y^2}{x^{12}}[/tex]
4. [tex]\rm 30x^{m+7}y^{n+4}[/tex]
5. [tex]\rm 8x^{a+b}y^{c+d}[/tex]
Step-by-step explanation:
1.
[tex]\rm 8^{-3} \times 8^7[/tex]
[tex]\implies 8^{-3+7}[/tex]
[tex]\implies {8^4}[/tex]
[tex]\implies \boxed{4096}[/tex]
2.
[tex]\rm (-3x^{-4})(25x^{-10})[/tex]
[tex]\implies \rm (-3)(25) \times (x^{-4})(x^{-10})[/tex]
[tex]\implies \rm -75 \times (x^{-4 + -10})[/tex]
[tex]\implies \rm -75x^{-14}[/tex]
[tex]\implies \rm -75 \times \frac{1}{x^{14}}[/tex]
[tex]\implies \boxed{\rm -\frac{75}{x^{14}}}[/tex]
3.
[tex]\rm (5x^{-3}y^4)(-2x^{-9}y^{-2})[/tex]
[tex]\implies \rm 5(-2) \times (x^{-3})(x^{-9}) \times (y^4)(y^{-2})[/tex]
[tex]\implies \rm -10 \times x^{-3 + (-9)} \times y^{4+(-2)}[/tex]
[tex]\implies \rm -10 \times x^{-12} \times y^2[/tex]
[tex]\implies \rm -10 \times \frac{1}{x^{12}} \times y^2[/tex]
[tex]\implies \boxed{\rm -\frac{10y^2}{x^{12}}}[/tex]
4.
[tex]\rm (5x^{m}y^{n})(6x^7y^4)[/tex]
[tex]\implies \rm 5(6) \times (x^{m})(x^7) \times (y^n)(y^4)[/tex]
[tex]\implies \rm 30 \times x^{m + 7} \times y^{n+4}[/tex]
[tex]\implies \boxed{\rm 30x^{m+7}y^{n+4}}[/tex]
5.
[tex]\rm -4(x^ay^c) \circ -2(x^by^d)[/tex]
[tex]\implies \rm -4(-2) \times (x^a)(x^b) \times (y^c)(y^d)[/tex]
[tex]\implies \rm 8 \times x^{a+b} \times y^{c+d}[/tex]
[tex]\implies \boxed{\rm 8x^{a+b}y^{c+d}}[/tex]
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