Question

11) 3 умножить (-4)⁻²+5⁻¹ 12)(-2,7)⁰+(1/7)⁻¹

Answer 1

$11)3 \times ( - 4) {}^{ - 2} + 5 {}^{ - 1} \\ 3 \times 4 { }^{ - 2} + \frac{1}{5} \\ \\ 3 \times \frac{1}{4 {}^{2} } + \frac{1}{5} \\ \\ 3 \times \frac{1}{16} + \frac{1}{5} \\ \\ \frac{3}{16} + \frac{1}{5} \\ \\ \frac{15 + 16}{80} \\ \\ \frac{31}{80} \\ \\ \\ 12)( - 2.7) {}^{0} + ( \frac{1}{7} ) {}^{ - 1} \\ \\1 + ( \frac{1}{7} ) {}^{ - 1} \\ \\ 1 + 7 = 8 \\ 8.$
12)любое отличное от нуля выражение,возведенное в степень 0,равно 1

Answer 2

To solve these expressions, let's follow the order of operations, which is usually expressed as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition, and Subtraction).

1. $3 \times (-4)^{-2} + 5^{-1}$

First, let's simplify the exponents inside the parentheses:

$3 \times (-4)^{-2} = 3 \times \frac{1}{(-4)^2} = 3 \times \frac{1}{16} = \frac{3}{16}$

Next, simplify $5^{-1}$:

$5^{-1} = \frac{1}{5}$

Now, put it all together:

$\frac{3}{16} + \frac{1}{5}$

To add these fractions, we need a common denominator, which is 80. So, we'll rewrite each fraction with a denominator of 80:

$\frac{3}{16} = \frac{3 \times 5}{16 \times 5} = \frac{15}{80}$

$\frac{1}{5} = \frac{1 \times 16}{5 \times 16} = \frac{16}{80}$

Now, add the fractions:

$\frac{15}{80} + \frac{16}{80} = \frac{31}{80}$

The final result is $\frac{31}{80}$.

2. $(-2.7)^0 + \left(\frac{1}{7}\right)^{-1}$

Any number raised to the power of 0 is equal to 1. So, $(-2.7)^0 = 1$.

Now, simplify $\left(\frac{1}{7}\right)^{-1}$:

$\left(\frac{1}{7}\right)^{-1} = 7$

Now, put it all together:

$1 + 7 = 8$

The final result is 8.