Question

1)5^-6*5^3/5^-5= 2)(7*10^-4)(1,4*10^2)= 3) 21^8*3^-6/7^7= 4)7*10^3+5*10^2+8*10^-1= 5) 2,4*10^2/8*10^-1=

Answer 1

1)5^-6*5^-3/5^-5=5^-8 2)

Answer 2

1) (1/5^3*5^3)/1/5^5=1/5^3*5^5=5^2=25
2) 7*1/10^4*140=98/10^3=0.098
3)21^8*7^7*3^6
4)7000+500+0.8=7500.8
5)240/0.8=300

Answer 3

Sure, I can help you simplify these expressions:

1. $\frac{5^{-6} \cdot 5^3}{5^{-5}}$ When you have the same base raised to different exponents, you can apply the rules of exponents. The rule here is $a^m \cdot a^n = a^{m+n}$, and $a^m / a^n = a^{m-n}$.

So, in this case: $5^{-6} \cdot 5^3 = 5^{-6 + 3} = 5^{-3}$ $5^{-6} / 5^{-5} = 5^{-6 - (-5)} = 5^{-1}$

Putting it all together: $\frac{5^{-6} \cdot 5^3}{5^{-5}} = 5^{-3} \cdot 5^1 = 5^{-3 + 1} = 5^{-2}$

2. $(7 \cdot 10^{-4})(1.4 \cdot 10^2)$ When multiplying numbers in scientific notation, you can simply multiply the coefficients and add the exponents of the same base.

$7 \cdot 1.4 = 9.8$ (coefficient multiplication) $10^{-4} \cdot 10^2 = 10^{-4 + 2} = 10^{-2}$ (exponent addition)

Putting it all together: $(7 \cdot 10^{-4})(1.4 \cdot 10^2) = 9.8 \cdot 10^{-2}$

3. $\frac{21^8 \cdot 3^{-6}}{7^7}$ Apply the rules of exponents again:

$21^8 / 7^7 = \frac{21^8}{21^7} = 21^{8-7} = 21$ $21^8 \cdot 3^{-6} = 21^8 \cdot (1/3^6) = 21^8 \cdot 3^{-6}$

Putting it all together: $\frac{21^8 \cdot 3^{-6}}{7^7} = \frac{21 \cdot 21^8 \cdot 3^{-6}}{1} = 21^9 \cdot 3^{-6}$

4. $7 \cdot 10^3 + 5 \cdot 10^2 + 8 \cdot 10^{-1}$ Simply add the terms:

$7 \cdot 10^3 = 7000$ $5 \cdot 10^2 = 500$ $8 \cdot 10^{-1} = 8$

Adding everything up: $7 \cdot 10^3 + 5 \cdot 10^2 + 8 \cdot 10^{-1} = 7000 + 500 + 8 = 7508$

5. $\frac{2.4 \cdot 10^2}{8 \cdot 10^{-1}}$ When dividing numbers in scientific notation, you can divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator.

$2.4 / 8 = 0.3$ (coefficient division) $10^2 / 10^{-1} = 10^{2 - (-1)} = 10^3$ 0 0