Question

9,10 Найдите значения выражения: 1)17^7*17^-4/17^-3 2) -0,7^7*0,7^-3/0,7^3*3 3)0,5^4*2^5/4^2:8^2 4)1,33^-5*1,33^6:p^0

Answer 1

$\displaystyle \tt 1). \ \ \frac{17^{7}\cdot 17^{-4}}{17^{-3}}=17^{7}\cdot 17^{-4}\cdot 17^{3}=17^{7-4+3}=17^{6};\\\\\\2). \ \ \frac{-0,7^{7}\cdot 0,7^{-3}}{0,7^{3}\cdot 3}=-\frac{1}{3}\cdot 0,7^{7}\cdot 0,7^{-3}\cdot 0,7^{-3}=-\frac{1}{3}\cdot 0,7^{7-3-3}=\\\\. \ \ \ =-\frac{1}{3}\cdot \frac{7}{10}=-\frac{7}{30};$

$\displaystyle \tt 3). \ \ \frac{0,5^{4}\cdot 2^{5}}{4^{2}:8^{2}}=\frac{2^{-4}\cdot 2^{5}\cdot 2^{6}}{2^{4}}=2^{-4+5+6-4}=2^{3}=8;\\\\\\4). \ \ 1,33^{-5}\cdot 1,33^{6}:p^{0}=1,33^{-5}\cdot 1,33^{6}:1=1,33^{6-5}=1,33;$

Answer 2

1) 17^7*17^-4/17^-3=17^(7-4+3)=17^6

2) -0,7^7*0,7^-3/0,7^3*3=-0,7^(7-3-3*3)=-0,7^-5

3)0,5^4*2^5/4^2:8^2=2^-4*2^5*2^-4*2^6=2^3=8

4)1,33^-5*1,33^6:p^0 = 1,33^(-5+6)*1 = 1,33

Answer 3

To simplify each expression, remember the following exponent rules:

1. When you have the same base raised to different exponents, you can apply the rules of exponents: a^m * a^n = a^(m + n) and a^m / a^n = a^(m - n).
2. Any non-zero number raised to the power of 0 is always equal to 1: a^0 = 1.

Now let's simplify each expression:

1. 17^7 * 17^-4 / 17^-3

Apply the rule a^m * a^n = a^(m + n) for the first part and a^m / a^n = a^(m - n) for the second part:

= 17^(7 - 4) / 17^(-3) = 17^3 * 17^3 (Negative exponent becomes positive when moved to the denominator) = 4913

2. -0.7^7 * 0.7^-3 / (0.7^3 * 3)

Apply the rule a^m * a^n = a^(m + n) and a^m / a^n = a^(m - n):

= -0.7^(7 - 3) / (0.7^3 * 3) = -0.7^4 / (0.7^3 * 3)

3. 0.5^4 * 2^5 / 4^2 : 8^2

Resolve the powers first:

= 0.0625 * 32 / 16 : 64 = 2 * 2 = 4

4. 1.33^-5 * 1.33^6 / p^0

Any non-zero number raised to the power of 0 is 1:

= 1.33^-5 * 1.33^6 / 1 = 1.33^(6 - 5) = 1.33^1 = 1.33

Please note that if any value of the variable 'p' is provided, you can substitute it into the expression to get the final result. If 'p' is not given, the expression will remain in terms of 'p'.