Answer:
80.
Step-by-step explanation:
x^2y^3 * x^3y^2
= x^(2+3)y^(3+2)
= x^5y^5 and as x^2y^3 = 10 and x^3y^2 = 8 we have:
10 * 8
= 80.
By using multiplication rule of exponential formulas, the value of [tex]x^{5} y^{5} =80[/tex].
When multiplying exponential expressions that have the same base, add the exponents. When dividing exponential expressions that have the same base, subtract the exponents. When raising an exponential expression to a new power, multiply the exponents.
Given equations
[tex]x^{2} y^{3} =10[/tex]...(1)
[tex]x^{3}y^{2} =8[/tex]...(2)
By multiplying equations 1 and 2
[tex]x^{2} y^{3} \times x^{3}y^{2} = 10 \times 8[/tex]
⇒ [tex]x^{2} \times y^{3} \times x^{3} \times y^{2} = 80[/tex]
⇒ [tex]x^{2} \times x^{3} \times y^{3} \times y^{2} = 80[/tex]
It is in the form of multiplication rule of exponential formula [tex]a^{m} \times a^{n} =a^{m+n}[/tex]
⇒ [tex]x^{2+3} \times y^{3+2} = 80[/tex]
⇒ [tex]x^{5} y^{5} =80[/tex]
Hence, the value of [tex]x^{5} y^{5} =80[/tex]
Find out more information about multiplication rule of exponential formulas here
https://brainly.com/question/23418174
#SPJ3
