Question

А) (3^-2)^4 2.Упростить выражения а)(a^-3)^5 * a^18 б)2,4х^-8 y^5 * 5x^9 y^-7

Answer 1

$1)(3 ^{-2} )^4=3 ^{-8} =1/6561$
$a ^{-15} *a ^{18} =a^3$
$3)12xy ^{-2} =12x/y^2$

Answer 2

1. (3^-2)^4: To simplify this expression, we need to apply the exponentiation rules. When raising a power to another power, we multiply the exponents. In this case, we have:

(3^-2)^4 = 3^(-2*4) = 3^-8

The negative exponent indicates that we need to take the reciprocal of the base raised to the positive exponent. So, we have:

3^-8 = 1/(3^8) = 1/6561

Therefore, (3^-2)^4 simplifies to 1/6561.

a) (a^-3)^5 * a^18: To simplify this expression, we apply the exponentiation rules. When raising a power to another power, we multiply the exponents. In this case, we have:

(a^-3)^5 * a^18 = a^(-3*5) * a^18 = a^-15 * a^18

Now, when multiplying two terms with the same base, we add their exponents:

a^-15 * a^18 = a^(-15 + 18) = a^3

Therefore, (a^-3)^5 * a^18 simplifies to a^3.

б) 2.4x^-8 y^5 * 5x^9 y^-7: To simplify this expression, we apply the multiplication and exponentiation rules. When multiplying two terms with the same base, we add their exponents. In this case, we have:

2.4x^-8 y^5 * 5x^9 y^-7 = (2.4 * 5) * (x^-8 * x^9) * (y^5 * y^-7)

2.4 * 5 = 12

Now, let's simplify the x-terms:

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

Finally, let's simplify the y-terms:

y^5 * y^-7 = y^(5 - 7) = y^-2 = 1/y^2

Putting it all together, we have:

2.4x^-8 y^5 * 5x^9 y^-7 = 12xy/y^2

So, the simplified expression is 12xy/y^2.